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Sub 505 (Easy)|   Algebra|      
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Bunuel
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If the cube of n is 180 greater than the square of n, then n = 08 May 2018, 04:25
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E
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89% (01:38) correct 11% (02:08) wrong based on 114 sessions

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If the cube of n is 180 greater than the square of n, then n =

(A) 10
(B) 9
(C) 8
(D) 7
(E) 6
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E
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If the cube of n is 180 greater than the square of n, then n = 08 May 2018, 04:32
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n^3=n^2+180

only n= 6 satisfies the equation
IMO answer should be E
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If the cube of n is 180 greater than the square of n, then n = 08 May 2018, 04:34
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Bunuel
If the cube of n is 180 greater than the square of n, then n =

(A) 10
(B) 9
(C) 8
(D) 7
(E) 6
Show more

\(n^3=n^2+180\)
Do not try to solve it, because it will consume a lot of time.

The simplest way to solve is as follows.

Since, \(n*n(n-1)=180\), \(n^3\) is slightly more than \(180\).

Cubes: \(1, 8, 64, 125, 216\)

\(216\) is slightly more than \(180\). So \(n^3=216\) and \(n=6\).

Answer: E
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If the cube of n is 180 greater than the square of n, then n = 08 May 2018, 04:51
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Apart from checking options and approximation, it can also be solved using factorization of the expression:

\(n^3 - n^2\) = 180
Or, \(n^3 - n^2\) - 180 = 0
Or, \(n^3 - 6n^2 + 5n^2\) - 30n + 30n - 180 = 0
Or, \(n^2\) (n - 6) + 5n (n - 6) + 30 (n - 6) = 0
Or, (n - 6) (\(n^2\)+ 5n + 30) = 0
from here only, we can say n = 6, as \(n^2\) + 5n + 30 is always > 0 for any positive value of n

Hence, correct answer is Option E
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If the cube of n is 180 greater than the square of n, then n = 09 May 2018, 00:58
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Bunuel
If the cube of n is 180 greater than the square of n, then n =

(A) 10
(B) 9
(C) 8
(D) 7
(E) 6
Show more


Though I totally messed his question, I would try to add my learning.

n^3 = n^2 + 180

n^3 - n^2 = 180 (Don't try to make a polynomial from here)

Now try answer choices one by one:

A. 10^3 - 10^12 = 180

900 = 180 (Incorrect)

E. 6^3 - 6^2 = 180

216 - 36 = 180

180 = 180 (Correct)

Hence (E)
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If the cube of n is 180 greater than the square of n, then n = 09 May 2018, 16:33
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Bunuel
If the cube of n is 180 greater than the square of n, then n =

(A) 10
(B) 9
(C) 8
(D) 7
(E) 6
Show more

We can create the equation:

n^3 = 180 + n^2

n^3 - n^2 - 180 = 0

We can see that it’s not easy to factor n^3 - n^2 - 180. Therefore, we will just check the answer choices and see which one satisfies the equation. Notice the cube root of 180 is less than 6 (because 6^3 = 216), so we’ll try the answer choices in reverse. That is, we’ll try answer choice E first.

If n = 6, then 6^3 - 6^2 - 180 = 216. - 36 - 180 = 0.

We see that we’ve found our answer.

Answer: E
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If the cube of n is 180 greater than the square of n, then n = 14 Jun 2019, 22:11
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Bunuel
If the cube of n is 180 greater than the square of n, then n =

(A) 10
(B) 9
(C) 8
(D) 7
(E) 6
Show more

Given n^3 = 180 + n^2
—> n^3 - n^2 = 180
—> n^2(n - 1) = 180 = 36*5
—> n^2*(n - 1) = 6^2*(6 - 1)

So, n = 6.

IMO Option E

Pls Hit kudos if you like the solution

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If the cube of n is 180 greater than the square of n, then n = 19 Jul 2024, 11:03
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